Speed Converter

What this calculates

Enter a speed in metres per second, kilometres per hour, miles per hour, feet per second or knots, and this shows it in all five at once, with each conversion worked through. It also places the speed on a scale running from 0.1 m/s to 1,000 m/s, each band shown in km/h as well, so the size of a speed can be read at a glance.

Every figure comes from exact definitions — nothing is converted with a rounded shortcut factor.

The formula

Every conversion goes through metres per second: into metres per second with one unit's size, then out again with another's.

Each unit is a distance over a time, and each is exact.

A kilometre per hour and a knot do not come out as terminating decimals in metres per second. The working shows such a figure to ten significant figures, marked ≈, while every result is worked out from the exact value — which is why 1 kn comes out as exactly 1.852 km/h.

Worked example

Some conversions come out exact. 60 mph is 60 × 0.44704 = 26.8224 m/s, which is exactly 96.56064 km/h and exactly 88 ft/s. 10 m/s is exactly 36 km/h.

When to use it, and the mistakes to avoid

Use it when a speed is given in a unit you do not think in, when comparing figures quoted in km/h with figures in mph, when a speed in metres per second needs to be read in kilometres per hour, and when a speed is given in knots.

The mistakes that cost the most:

• Dividing by 3.6 when you should multiply. Metres per second to kilometres per hour is × 3.6: 10 m/s is 36 km/h. Kilometres per hour to metres per second is ÷ 3.6: 100 km/h is 27.77778 m/s. Use the wrong one and the answer is far too small or far too large — a quick check is that the km/h figure is always the bigger one.
• Using × 1.6 as if it were exact. The mile is 1.609344 km, not 1.6. The rough rule turns 60 mph into 96 km/h against the true 96.56064 km/h, and 100 km/h into 62.5 mph against the true 62.13712 mph. Close for a rough sense of speed, but not an answer.
• Saying "knots per hour". A knot is already a speed — one nautical mile an hour — so "per hour" would make it a change in speed. And a nautical mile is 1,852 m, not a mile: 1 kn is 1.852 km/h but 1.150779 mph.
• Expecting every digit of every result. Results are shown to seven significant figures — 100 km/h shows as 62.13712 mph — while each is worked out from the exact value. A speed far too small for a unit, such as 0.000000000000001 ft/s in metres per second, reads as 0, and a note under the result says so rather than leaving a silent zero.
• Entering a negative speed. A speed here is how fast, not which way, so the calculator refuses a negative one with a message instead of converting it.

FAQ